Speaker
Description
Lieb–Schultz–Mattis anomalies and gauging connect anomalous lattice systems to topologically ordered quantum codes with position-dependent symmetries. Motivated by this connection, we study what weak measurements can reveal about the information stored in such codes. The measurement outcomes are treated as data for inferring hidden error configurations, translating the quantum problem into a classical statistical model. At a higher Nishimori condition, an enlarged symmetry gives exact relations between information inferred from the measurement outcomes and correlations in the unmeasured system. For the rank-2 toric code and X-cube model, these relations show that measurements can reveal dipole and subsystem order, respectively, rather than ordinary local order.